Quasi-Nelson Algebras

Abstract We introduce a generalization of Nelson algebras having a not-necessarily involutive negation; we suggest to dub this class quasi-Nelson algebras in analogy with quasi-De Morgan lattices, these being a non-involutive generalization of De Morgan lattices. We show that, similarly to the involutive case (and perhaps surprisingly), our new class of algebras can be equivalently presented as (1) quasi-Nelson residuated lattices, i.e. models of the well-known Full Lambek calculus with exchange and weakening, extended with the Nelson axiom; (2) non-involutive twist-structures, i.e. special products of Heyting algebras, which generalize the well-known construction for representing algebraic models of Nelson's constructive logic with strong negation; (3) quasi-Nelson algebras, i.e. models of non-involutive Nelson logic viewed as a conservative expansion of the negation-free fragment of intuitionistic logic. The equivalence of the three presentations, and in particular the extension of the twist-structure representation to the non-involutive case, is the main technical result of the paper. We hope, however, that the main impact may be the possibility of opening new ways to (i) obtain deeper insights into the distinguishing feature of Nelson's logic (the Nelson axiom) and its algebraic counterpart; (ii) be able to investigate certain purely algebraic properties (such as 3-potency and (0,1)-congruence orderability) in a more general setting

Discriminator logics (Research announcement)

A discriminator logic is the 1-assertional logic of a discriminator variety V having two constant terms 0 and 1 such that V ⊨ 0 1 iff every member of V is trivial. Examples of such logics abound in the literature. The main result of this research announcement asserts that a certain non-Fregean deductive system SBPC, which closely resembles the classical propositional calculus, is canonical for the class of discriminator logics in the sense that any discriminator logic S can be presented (up to definitional equivalence) as an axiomatic extension of SBPC by a set of extensional logical connectives taken from the language of S. The results outlined in this research announcement are extended to several generalisations of the class of discriminator logics in the main work

The Logic of Quasi-MV Algebras

The algebraic theory of quasi-MV algebras, generalizations of MV algebras arising in quantum computation, is by now rather well-developed. Although it is possible to define several interesting logics from these structures, so far this aspect has not been investigated. The present article aims at filling this ga

Discriminator logics (Research announcement)

A discriminator logic is the 1-assertional logic of a discriminator variety V having two constant terms 0 and 1 such that V ⊨ 0 1 iff every member of V is trivial. Examples of such logics abound in the literature. The main result of this research announcement asserts that a certain non-Fregean deductive system SBPC, which closely resembles the classical propositional calculus, is canonical for the class of discriminator logics in the sense that any discriminator logic S can be presented (up to definitional equivalence) as an axiomatic extension of SBPC by a set of extensional logical connectives taken from the language of S. The results outlined in this research announcement are extended to several generalisations of the class of discriminator logics in the main work

Hydrogels containing the ferri/ferrocyanide redox couple and ionic liquids for thermocells

Thermoelectrochemical cells are a promising new technology for harvesting low-grade waste heat. The operation of these cells relies on a redox couple within an electrolyte, which is most commonly water-based, and improvement of these materials is a key aspect of the advancement of this technology. Here, we report the gelation of aqueous electrolytes containing the K3Fe(CN)6/K4Fe(CN)6 redox couple using a range of different polymers, including polyvinyl alcohol (PVA), sodium carboxymethyl cellulose (Cmc), polyacrylamide (PAAm), and two commercial polyurethane-based polymers: HydroMed D640 and HydroSlip C. These polymers produce quasi-solid-state electrolytes with sufficient mechanical properties to prevent leakage, and allow improved device flexibility and safety. Furthermore, the incorporation of various ionic liquids within the optimized hydrogel network is investigated as a route to enhance the electrochemical and mechanical properties and thermal energy harvesting performance of the hydrogels

Emerging nuclear collectivity in 124-130Te

The emergence of nuclear collectivity near doubly-magic 132Sn was explored along the stable, eveneven 124−130Te isotopes. Preliminary measurements of the B(E2; 41+ → 21+) transition strengths are reported from Coulomb excitation experiments primarily aimed at measuring the g factors of the 41+ states. Isotopically enriched Te targets were excited by 198-205 MeV 58Ni beams. A comparison of transition strengths obtained is made to large-scale shell-model calculations with successes and limitations discussed

Operationalizing marketable blue carbon

The global carbon sequestration and avoided emissions potentially achieved via blue carbon is high (∼3% of annual global greenhouse gas emissions); however, it is limited by multidisciplinary and interacting uncertainties spanning the social, governance, financial, and technological dimensions. We compiled a transdisciplinary team of experts to elucidate these challenges and identify a way forward. Key actions to enhance blue carbon as a natural climate solution include improving policy and legal arrangements to ensure equitable sharing of benefits; improving stewardship by incorporating indigenous knowledge and values; clarifying property rights; improving financial approaches and accounting tools to incorporate co-benefits; developing technological solutions for measuring blue carbon sequestration at low cost; and resolving knowledge gaps regarding blue carbon cycles. Implementing these actions and operationalizing blue carbon will achieve measurable changes to atmospheric greenhouse gas concentrations, provide multiple co-benefits, and address national obligations associated with international agreements